A Knowledge-Inspired Hierarchical Physics-Informed Neural Network for Pipeline Hydraulic Transient Simulation

TL;DR

This work tackles hydraulic transient simulation in high‑pressure, multi‑product pipelines, where traditional model‑driven and data‑driven methods struggle with efficiency, accuracy, and explainability. It introduces Knowledge‑Inspired Hierarchical PINN (KIH‑PINN), which encodes governing 1D transient flow equations, boundary and initial conditions, and uses magnitude conversion to harmonize output scales, coupled with a staged training strategy to balance gradients. On a simulated pipeline system, KIH‑PINN outperforms a DNN and a standard PINN, achieving substantially lower RMSE and MAPE for pressure predictions and robust performance under complex transient conditions, with residuals around $0.01$ MPa and R² near 1.0. The approach enhances computational efficiency and physical consistency, supporting safer, more reliable pipeline operation, and highlights future work on inverse problems for parameter identification.

Abstract

The high-pressure transportation process of pipeline necessitates an accurate hydraulic transient simulation tool to prevent slack line flow and over-pressure, which can endanger pipeline operations. However, current numerical solution methods often face difficulties in balancing computational efficiency and accuracy. Additionally, few studies attempt to reform physics-informed learning architecture for pipeline transient simulation with magnitude different in outputs and imbalanced gradient in loss function. To address these challenges, a Knowledge-Inspired Hierarchical Physics-Informed Neural Network is proposed for hydraulic transient simulation of multi-product pipelines. The proposed model integrates governing equations, boundary conditions, and initial conditions into the training process to ensure consistency with physical laws. Furthermore, magnitude conversion of outputs and equivalent conversion of governing equations are implemented to enhance the training performance of the neural network. To further address the imbalanced gradient of multiple loss terms with fixed weights, a hierarchical training strategy is designed. Numerical simulations demonstrate that the proposed model outperforms state-of-the-art models and can still produce accurate simulation results under complex hydraulic transient conditions, with mean absolute percentage errors reduced by 87.8\% and 92.7 \% in pressure prediction. Thus, the proposed model can conduct accurate and effective hydraulic transient analysis, ensuring the safe operation of pipelines.

Figures (8)

• Figure 1: Schematic diagram of variations in pipeline pressure and flowrate
• Figure 2: Pipeline schematic diagram in practical
• Figure 3: Comparison of magnitude between velocity and head
• Figure 4: The framework of the proposed knowledge-inspired physics-informed neural network
• Figure 5: The diagrammatic sketch of the SPS simulation model of a pipeline system